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摘要翻译：
受领地浮现的集体现象的启发，动物通过它们沉积的气味标记移动和相互作用，我们研究了一维布朗行者在随机环境中的动力学，随机环境包括自己反常扩散的有限边界。本文给出了如何在一定的参数条件下，将领土性的非马尔可夫多体问题简化为本文所研究的解析可处理的单体问题。精确地计算了一维Brownian walker在亚扩散边界内的均方位移(MSD)，推广了边界不动时的已知结果。此外，在一定的条件下，如果边界动力学是强次扩散的，我们在MSD的时间依赖中表现出一个有趣的非单调性，从而引起瞬态负扩散。
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英文标题：
《Brownian walkers within subdiffusing territorial boundaries》
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作者：
Luca Giuggioli, Jonathan R. Potts, Stephen Harris
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最新提交年份：
2011
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分类信息：
一级分类：Physics 物理学
二级分类：Mathematical Physics 数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics 数学
二级分类：Mathematical Physics 数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
Inspired by the collective phenomenon of territorial emergence, whereby animals move and interact through the scent marks they deposit, we study the dynamics of a 1D Brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously. We show how to reduce, in certain parameter regimes, the non-Markovian, many-body problem of territoriality to the analytically tractable one-body problem studied here. The mean square displacement (MSD) of the 1D Brownian walker within subdiffusing boundaries is calculated exactly and generalizes well known results when the boundaries are immobile. Furthermore, under certain conditions, if the boundary dynamics are strongly subdiffusive, we show the appearance of an interesting non-monotonicity in the time dependence of the MSD, giving rise to transient negative diffusion.
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PDF链接：
https://arxiv.org/pdf/1102.0966
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